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arXiv · 1810.06927

A note on locally elliptic actions on cube complexes

Nils Leder·Olga Varghese
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Abstract

We deduce from Sageev's results that whenever a group acts locally elliptically on a finite dimensional CAT(0) cube complex, then it must fix a point. As an application, we give an example of a group G such that G does not have property (T), but G and all its finitely generated subgroups can not act without a fixed point on a finite dimensional CAT(0) cube complex, answering a question by Barnhill and Chatterji.

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Nils Leder, Olga Varghese. 2018-10-16. A note on locally elliptic actions on cube complexes. https://doi.org/10.2140/iig.2020.18.1

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